utility theory & prospect theory

7/30/2019 Utility Theory & Prospect Theory

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1012/2013Behavioral Finance

Chapter 6Prospect Theory


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Theory for decision making under risk

Normative Theory

Expected Utility Theory(von Neumann and Morgenstern, 1944)

Objective probability judgment

A set of intuitive axioms

Roots to be found in Bernoulli

(1738)

Descriptive Theory

Prospect Theory(Kahneman and Tversky, 1979)

Explicitly not normative

Positive application (summarizes

what people actually do)

Probably the most widely cited

(influential) social science paper

ever published

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Advice how you should decide Prediction of what you will decide


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Prospect Theory

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Editing Phase

Choice problem

Evaluation Phase

Probability

weighting Value Function

Decision

Prospect theory is strictly defined for choice

situations involving risk, although it has found its

way into other disciplines as well (e.g. marketing)

This is the preparation before options are evaluated.

Based on perception and psychological processes,

the presented information is organized.

This the link between observing information and

performing a choice. In contrast to expected utility

theory, risk is evaluated on two different dimensions.

(1) Probabilities and (2) payoffs

In contrast to normative choice theories, the goal of

prospect theory is to provide good prediction of

choices


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Editing Phase: Coding

In contrast to expected utility theory, decision makers do not consider their final

wealth. They consider gains and losses compared to a reference point.

During the editing phase, decision makers will decide what reference point to use

(e.g. opportunity cost, minimum wage requirement, etc.)

The payoffs of the lottery will then be coded as a gain or a loss

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Choice Problem Modification

Option L

200.50

Option S

10

Expected

earnings in an

experiment

10

Option L

100.5-10

Option S

0

or

Reference Point

orEvaluation

Phase

Coding


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Editing Phase: Combination

In the evaluation phase, as in expected utility theory, only payoffs and

probabilities are considered

Therefore, probabilities of events with identical outcomes are combined

to one event.

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Choice Problem

Option L

20E1(0.1)20E2(0.5)0

Option S

10

Option L

200.60

Option S

10

or

Reduction to Payoffs and Probabilities

orEvaluation

Phase

Combination


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Editing Phase: Simplification

People have difficulties to pick up small numerical differences in

probabilities and payoffs

For both, probabilities and payoffs, are modified to simpler numbers

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Choice Problem

Option L

210.490

Option S

10

Option L

200.50

Option S

10

or

Rounding up/down to simpler numbers

orEvaluation

Phase

Simplification


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Editing Phase: Segregation

People perceive situations involving risk different than situations involving

sure outcomes (i.e. sure payoffs are not risky payoffs with probability 1)

Sure gains are segregated from the lottery, the same is true for sure losses

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Choice Problem

Option L

300.2510

Option S

15

Option L

10 + 200.250

Option S

15

or

Disentangle safe from risky payoffs

orEvaluation

Phase

Segregation


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Editing Phase: Cancellation (Type I)

People focus on differences rather than similarities when evaluating

prospects

Equal payoffs of two options are therefore not considered when

performing a choice (are considered not to have an influence on wealth)

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Choice Problem

Option L

200.250.5-5

Option S

200.2150.5-10

Option L

00.250.5-5

Option S

00.2150.5-10

or

Identical payoffs are not considered

orEvaluation

Phase

Cancellation


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Editing Phase: Cancellation (Type II)

In expected utility theory we have the Reduction of Compound Lotteries

axiom

In prospect theory: two-stage lotteries are reduced to the reduced form

If in the first stage one payoff is zero, the first stage is neglected all

together

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Two-stage Lottery Neglecting of the first stage

Evaluation

Phase

Cancellation

0

20

000.25

0.75

0.8

0.2

20

00

0.8

0.2

h l


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Editing Phase

Note:

The sequence of editing

procedures may differ between

decision makers and choice

problems

The sequence of editingprocedures probably depends on

the task and framing of the

choice problem

The application of some editing

procedures may prevent othersfrom being applied

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Coding

Combination

Simplification

Segregation

Cancellation

B h i l Fi


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Note down your decisions for the following scenario

Story: 600 people are attacked by a fatal disease

Choice: Which program would you prefer

Program A: Saving 200 lives for sure

Program B: Saving 600 lives with 1/3 probability

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S1

B h i l Fi


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Program A: Losing 400 lives for sure

Program B: Losing 600 lives with 2/3 probability

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S2

Behavioral Finance


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Story: Imagine that you have just been given 1000 Euro

Choice: Which option would you prefer

Option A: You receive 500 Euro for sure

Option B: You receive 1000 Euro with 50% chance

and nothing otherwise

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S3

Behavioral Finance


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Option A: You have to pay back 500 Euro for sure

Option B: You have to pay back 1000 Euro with 50% chance


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S4

Behavioral Finance


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Framing effect



Live-saving frame:

Program A: Saving 200 lives for sure Program B: Saving 600 lives with 1/3 probability

Live-losing frame:

Program A: Losing 400 lives for sure

Program B: Losing 600 lives with 2/3 probability

Program A and B are identical in both scenarios.

Only the Frame of choice tasks changes

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S1

S2

Blacked Out

To be revealed in the lecture

Behavioral Finance


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Framing Effect



Option A: You receive 500 Euro for sure

Option B: You receive 1000 Euro with 50% chanceand nothing otherwise



Option A: You have to pay back 500 Euro for sure

Option B: You have to pay back 1000 Euro with 50% chance


Option A and B are identical in both scenarios.

Only the Frame of choice tasks changes

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S3

S4

Blacked Out


Behavioral Finance


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Evaluation Phase: Value Function

Three characteristics

Decreasing marginal utility for

gains (risk-aversion), identical

to expected utility theory ()

Risk-seeking for losses ()

Loss-aversion, i.e. people

generally reject lotteries of the

form +X0.5-X ()

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Does loss aversion exist in expected utility theory?

Can you think of an experimental method to measure loss aversion?

Behavioral Finance


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Evaluation Phase: Probability Weighting

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Kahneman and Tversky, 1979 Kahneman and Tversky 1992



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e a o a a ce

Fourfold pattern of risk attitude

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Payoff

Probability

low high

risk-seeking

risk-averse risk-seeking

risk-averse

but not a new idea

(Friedman and Savage, 1948 )

and (Markowitz, 1952)

Implicit in Prospect Theory

(Kahneman and Tversky, 1979)



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What are the lessons learned in Chapter 6?

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Please take some time to compile a list of a few bullet points about

the most important facts you took from this chapter.

Check and discuss your list with that of your neighbor



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Lessons learned: Chapter 6

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There are two approaches in modeling decision making under risk

Normative (i.e. expected utility theory)

Descriptive (i.e. prospect theory)

Prospect theory consists of two processes

Editing phase (psychological biases concerning the numerical information) Evaluation Phase

Value function (similar to expected utility theory)

Probability function

Implication of evaluation phase: fourfold pattern of risk preferences

Blacked Out




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References: Chapter 6

Friedman, Milton and L. J. Savage (1948). The utility analysis of choices involving risk.

Journal of Political Economy, 56 (4), 297-304.

Kahneman, Daniel and Amos Tversky (1979). Prospect theory: An analysis of decision

under risk. Econometrica, 47 (2), 263-292.

Markowitz, Harry (1952). The utility of wealth. Journal of Political Economy, 60 (2),

151-158.

Neumann, John von and Oskar Morgenstern (1944). Theory of Games and Economic

Behavior. Princeton University Press: Princeton.

Tversky, Amos and Daniel Kahneman (1992). Advances in prospect theory: Cumulative

representation of uncertainty. Journal of Risk and Uncertainty, 5 (4), 297-323.

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